Truncated theta series related to the Jacobi Triple Product identity

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-14 DOI:10.1016/j.disc.2024.114319

Cristina Ballantine , Brooke Feigon

引用次数: 0

Abstract

The work of Andrews and Merca on the truncated Euler's pentagonal number theorem led to a resurgence in research on truncated theta series identities. In particular, Yee proved a truncated version of the Jacobi Triple Product (JTP) identity. Recently, Merca conjectured a stronger form of the truncated JTP identity. In this article we prove the first three cases of the conjecture and several related truncated identities. We prove combinatorially an identity related to the JTP identity which in particular cases reduces to identities conjectured by Merca and proved analytically by Krattenthaler, Merca and Radu. Moreover, we introduce a new combinatorial interpretation for the number of distinct 5-regular partitions of n.

查看原文本刊更多论文

与雅可比三乘积特性相关的截断θ级数

安德鲁斯（Andrews）和梅尔卡（Merca）在截断欧拉五边形数定理方面的工作，导致了截断θ级数特性研究的复苏。其中，Yee 证明了雅可比三乘积（JTP）特性的截断版本。最近，Merca 猜想出了截断 JTP 特性的更强形式。在本文中，我们证明了猜想的前三种情况和几个相关的截断标识。我们通过组合证明了一个与 JTP 特性相关的特性，在特定情况下，它还原了由梅尔卡猜想并由克拉滕塔勒、梅尔卡和拉杜分析证明的特性。此外，我们还为 n 的不同 5-regular 分割数引入了一种新的组合解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.